SarkariPYQ

SSC CGL 2024 PYQ — Question 51

SSC CGL - 26 Sep 2024 - Shift 3 • Quantitative Aptitude • Q51

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If cotθ=11cotθ=\sqrt11, then the value of cosec2θ−sec2θcosec2θ+sec2θ{cosec^2θ-sec^2θ}\over {cosec^2θ+sec^2θ} is:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 565\over6.

cot θ = √11 = √11/1 = Base/Height

Hypotenuse2 = (√11)2 + 12 = 11 + 1 = 12

⇒ Hypotenuse = √12 = 2√3

Now, (cosec2θ - sec2θ)/(cosec2θ + sec2θ)

= [(2√3)2 - (2√3/√11)2]/[(2√3)2 + (2√3/√11)2]

= [12 - (12/11)]/[12 + (12/11)]

= [(132 - 12)/11]/[(132 + 12)/11]

= (120/11)/(144/11)

= 120/144

= 5/6

Therefore, the value of the given expression is 5/6.